Heavy neutral leptons N are the most appealing candidates to generate the
tiny neutrino masses. In this paper, we study the signature of heavy neutral
leptons in gauged U(1)Lμ​−Lτ​​ at a muon collider. Charged under the
U(1)Lμ​−Lτ​​ symmetry, the heavy neutral leptons can be pair produced
via the new gauge boson Z′ at muon collider as μ+μ−→Z′∗→NN and μ+μ−→Z′(∗)γ→NNγ. We then perform a
detailed analysis on the lepton number violation signature μ+μ−→NN→μ±μ±W∓W∓ and μ+μ−→NNγ→μ±μ±W∓W∓γ at the 3 TeV muon collider, where the hadronic decays of
W boson are treated as fat-jets J. These lepton number violation signatures
have quite clean backgrounds at the muon collider. Our simulation shows that a
wide range of viable parameter space is within the reach of the 3 TeV muon
collider. For instance, with new gauge coupling g′=0.6 and an integrated
luminosity of 1000 fb−1, the μ±μ±JJ signal could probe
mZ′​≲12.5 TeV. Meanwhile, if the gauge boson mass satisfies 2mN​<mZ′​<s​, the μ±μ±JJγ signature would be more
promising than the μ±μ±JJ signature.Comment: 20 pages, 8 figures, 2 table